
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Ground state--excited state three-photon 
transition moments: \Sec{CCTM}}\label{sec:cctm}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
This Section describes the calculation of third-order transition
moments and strengths. Three photon transition strengths are defined:
\[
\small
S^{of}_{ABC,DEF}(\omega_1,\omega_2) = \frac{1}{2} 
       \{ M^{ABC}_{of}(-\omega_1,-\omega_2) M^{DEF}_{fo}(\omega_1,\omega_2)
        +[M^{DEF}_{of}(-\omega_1,-\omega_2) M^{ABC}_{fo}(\omega_1,\omega_2)]^\ast\}
\]
where $M^{ABC}_{of}(\omega_1,\omega_2)$ and $M^{ABC}_{fo}(\omega_1,\omega_2)$
are the left and right three photon transition moments, respectively.
The methodology is implemented for the CC models CCS, CC2 and CCSD.
Publications reporting results obtained with this module should cite~\cite{}.

\begin{description}
\item[\Key{OPERAT}] \verb| |\newline
\verb|READ (LUCMD,'(6A)') LABELA, LABELB, LABELC, LABELD, LABELE, LABELF|\newline
\verb|DO WHILE (LABELA(1:1).NE.'.' .AND. LABELA(1:1).NE.'*')|\newline
\verb|   READ (LUCMD,'(6A)') LABELA, LABELB, LABELC, LABELD, LABELE, LABELF|\newline
\verb|ENDDO|\newline   
Select the hexuples of operator labels for which to calculate the three-photon transition
moments. Operator hexuples which do not correspond to symmetry allowed combinations will be
ignored during the calculation.
\item[\Key{DIPOLE}] \verb| |\newline
Calculate the three photon moments and strengths for all possible combinations of cartesian 
components of the electric dipole moment operator (729 combinations).
\item[\Key{PRINT }] \verb| |\newline
\verb|READ (LUCMD,*) IPRTM|\newline
Read print level. Default is 0.
\item[\Key{SELSTA}] \verb| | \newline
\verb|READ (LUCMD,'(A70)') LABHELP|\newline
\verb|DO WHILE (LABHELP(1:1).NE.'.' .AND. LABHELP(1:1).NE.'*')|\newline
\verb|  READ (LUCMD,*) IXSYM, IXST, FREQB, FREQC|\newline
\verb|END DO| \newline
Select one or more excited states $f$ (among those specified
in \Sec{CCEXCI}), and the laser frequencies.
The symmetry (\verb+IXSYM+) and state number (\verb+IXST+)
within that symmetry are then given,
one pair (\verb|IXSYM,IXST|) per line.
\verb+FREQB+ and \verb+FREQC+ specify the 
laser frequencies $\omega_1$ and $\omega_2$ (in atomic units).


Default is all states specified in \Sec{CCEXCI}, and for each state
both laser frequencies equal to one third the excitation energy.

%
\item[\Key{THIRDF}]
Set the frequency arguments for the three-photon transition moments
equal to one third the excitation energy of the (chosen) 
final state $f$. Default, if \verb+FREQB,FREQC+ are not specified 
in \Key{SELSTA}.
%
\end{description}
